The question of what is the best item for each slot depends entirely on your build. I highly recommend using Beams and will focus this guide on them, but not everyone will want to use the same build for every character - variety is the spice of life, after all. If you use Torpedoes, the best items won't be the same as if you fly a Beam Boat. I can only answer this question specifically for certain builds, individually. (I don't know every possible build and it would be more clutter than anything if I were trying to give the best set for each and every individual build.) A generic answer would be almost useless because each build can have such different and specific needs. What I'd like to do is explain why I recommend each Item . To do that, I'll define what I feel is the best possible item in each slot for this build and why.
(Advanced Tip: I never recommend Cannons or Dual Cannons and you won't see a "best cannon build" on this site. In general, my chief issue with them is that they require proximity to the target in order to do full damage. Basically, the further away you are from the enemy you're shooting at, the less damage cannon-type weapons do. I also find that Cannon Rapid Fire isn't as effective as Fire at Will. I can't recommend Cannons to anyone as long as Beam Banks are available. If you are considering Beam Banks vs Dual Cannons, choose Beam Banks.)
Beam Boat - a ship that relies on Beam Arrays and/or Beam Banks for it's primary weapon damage, with at least 6 Beam Weapons.
Shield - Iconian Resistance Shield
Engine - Iconian Resistance Impulse Engines
Deflector - Iconian Resistance Deflector
Warp/Singularity Core - Iconian Resistance Warp/Singularity Cores (Must upgrade to get the [AMP] mod.)
Science Consoles - Fleet Science Consoles with "Plasma Explosion" mod OR Universal Consoles with Crit Chance and/or Crit Damage.
Tactical Consoles - Fleet Locator Tactical Consoles for your chosen energy type.
Engineering Consoles - Universal Consoles with Crit Chance and/or Crit Damage and a Plasmonic Leech console.
1. If using dual beam banks, you will need to use omnidirectional beam arrays on the rear of the ship. If you have three rear weapons, it is best to use Antiproton or Tetryon weapons due to the fact that omnis are unique and you can get the Ancient Antiproton Omni from the Dyson Sphere questline or a Tetryon Omni from the quest "Butterfly."
2. In general, the best crafted weapon types for damage are Antiproton and Disruptor. Plasma has been significantly nerfed and is not recommended at this time. Using Tetryon, Polaron, and Phaser will give consistently lower dps for Beam Boat builds. Tetryon, in particular, could be beneficial if not for the fact many enemies have no shields at all (such as Gateways or Transformers in Infected: The Conduit) and Tetryon literally has no beneficial effect against them. Outside of those instances, Tetryon is a fine choice. Polaron is similarly limited in dps, but its defensive benefits from the reduced weapon power of your enemy and it's use in PvP drain builds make it viable.
3. Many lockbox or reputation weapon types are fairly good for dps. I recommend Polarized Disruptors. Corrosive Plasma and Romulan Plasma are good choices for their type. Elachi Disruptors are semi-useful, but ultimately suffer from the fact that they ignore 50% of resistances - if the resistances have been debuffed to zero or lower by attack pattern beta... well 50% of zero Is zero. They would Ignore nothing. They are also outperformed by crafted Disruptors.
4. This shouldn't have to be said, but in case it's not known by anyone reading this, picking one energy type is essential. Shooting "Rainbows" (ie many different types of energy weapons) isn't optimal for damage. You could use +beam tactical consoles and make it work, but that is not optimal for dps, due in large part to the fact specialized enengy type consoles give larger bonuses to damage than generic +beam consoles do. You could use Romulan Plasma, Corrosive Plasma, and crafted Plasma weapons because they're all plasma and are all modified by the same plama-specific tactical consoles. It's when they aren't modified by the same tactical consoles that you have an issue.